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In a previous paper, Oruba, Soward & Dormy (J.Fluid Mech., vol.818, 2017,pp.205-240) considered the primary quasi-steady geostrophic (QG) motion of aconstant density fluid of viscosity $\nu$ that occurs during linear spin-downin a cylindrical container of radius $L$ and height $H$, rotating rapidly(angular velocity $\Omega$) about its axis of symmetry subject to mixed rigidand stress-free boundary conditions for the case $L=H$. Here, Direct NumericalSimulation (DNS) at large $L= 10 H$ and Ekman number $E=\nu/H^2\Omega=10^{-3}$reveals structured inertial wave activity on the spin-down time-scale. Theanalytic study, based on $E\ll 1$, builds on the results of Greenspan & Howard(J.Fluid Mech., vol.17, 1963, pp.385-404) for an infinite plane layer$L\to\infty$. At large but finite distance $r^\dag$ from the symmetry axis, themeridional (QG-)flow, that causes the QG-spin down, is blocked by the lateralboundary $r^\dag=L$, which provides a QG-trigger for inertial waves. The truesituation in the unbounded layer is complicated further by the existence of asecondary set of maximum frequency (MF) inertial waves (a manifestation of thetransient Ekman layer) identified by Greenspan & Howard. Their blocking at$r^\dag=L$ provides a secondary MF-trigger for yet more inertial waves that weconsider in a sequel (Part II). Here, for the QG-trigger, we solve a linearinitial value problem by Laplace transform methods. The ensuing complicatedinertial wave structure is explained analytically on approximating ourcylindrical geometry at large radius by rectangular Cartesian geometry, validfor $L-r^\star=O(H)$ ($L\gg H$). Other than identifying small scale structurenear $r^\star=L$, our main finding is that inertial waves radiated away fromthe outer boundary (but propagating towards it) reach a distance determined bythe group velocity.

The inertial wave activity during spin-down in a rapidly rotating penny shaped cylinder. Part I The quasi-geostrophic trigger